Download Midsegment Thm paragraph proof

Midsegment Theorem
GEOMETRY
NAME_________________________
DATE __________ Per.___________
Quadrilaterals
is the midpoint
1. M
of TR.
T
a) Measure each of
the following angles.
D is the
midpoint
of TI.
m ∠TMD =
m ∠MDT =
m ∠TRI =
m ∠RIT =
b) As these are corresponding angles, what can
you conclude?
M
D
c) Measure each of the following segments.
MD =
RI =
d) Notice anything special?
R
I
2. MIDSEGMENT THEOREM:
In any triangle, the segment joining the midpoints of any
two sides -- called the
-- is
to the
third side and
the length of that side.
3.
GIVEN:
MD is the midsegment of ∆ISE.
I
M
S
D
G
PROVE:
MD // SE and
MD = SE÷2
E
Extend MD to G so that MD ≅ DG. D is a midpoint of IE so ID ≅ ____.
Therefore, D is the midpoint of both ___ and ___. Since its diagonals
________ each other, quadrilateral MIGE is a ______________. Hence, GE
// IM by ___________ of a parallelogram. Since opposite sides of a
parallelogram are congruent, GE ≅ ___. Because M is a midpoint of ___, IM
≅ ___. Therefore, GE = MS by the _________ property. As GE // IM, ___
is also parallel to IS, and therefore, MS. With GE & MS being parallel and
congruent, SEGM is a _________. Hence, MG is __________ to SE by
definition of a ______________ so MD // SE since D is on MG.
MD = MG÷2 by the __________ Theorem, and MG ≅ ___ as opposite sides
of a parallelogram are congruent. Finally, MD = SE÷2 by _____________.